Purpose This project helps investigators to cope with complex equations that model biological systems. PROJECT 1:David Ruskin and Judy Walters, NINDS. In order to monitor variations in neuron firing rates in a live animal, this group wanted a MATLAB version of the Lomb periodogram, as published by Press et al. Numerical Recipes in C, Cambridge Univ. Press, Cambridge 1988. The authors describe this program as turgid code, and indeed, it took quite an effort to get it right. I wrote two MATLAB versions, one based on the above book, and a simpler but less efficient version based on a paper by Jeffrey Scargle: Astrophys. J. 263 (1982),835-853. The object was to allow complete control over the test cases to insure bug-free code. Once a working program was ready and real data began to arrive, two discouraging facts came to light. First, the lab didnt really need the program, because for their data, the finite Fourier transform does essentially the same job. I gave a seminar to their lab about this. Second, the method itself is flawed, and can give misleading information about the presence and power of a given frequency. I wrote a paper about a method for correcting the problem, and submitted it to the journal Astrophysics and Space Science, who published the original Lomb paper. PROJECT 2: Richard Hendler, NHLBI. Bacteriorhodopsin (bR)is an important biological energy transducer. It converts light into electrochemical potential by pumping protons across the cell membrane. bR is one of those molecules, like hemoglobin and cytochrome oxidase, in which a lot is known about the structure, but important aspects of the mechanism are still unclear. We are using mathematical modeling to decide the merits of several models that have appeared in the literature in recent years, including our own. The experiment consists of exposing bR to a laser flash, and measuring absorbance spectra as a function of time. We have developed new techniques that will enable investigators to extract more information from their data than was previously thought possible. For example, the fraction of bR reacting to the flash and the fraction in each of the fast and slow subcycles are now resolvable, along with absolute spectra rather than difference spectra. We have also discovered an artifact in the experiments as done by labs worldwide, including ours. We will be proposing methods to correct it. Mathematical analysis was crucial in spotting the artifact. PROJECT 3: P-SCAN The popular program P-SCAN for DNA microarray analysis is written mostly in MATLAB. I have been active in upgrading the performance of several P-SCAN functions. PROJECT 4: MATLABMATLAB is a popular commercial mathematical programming language involving hundreds of users at the NIH. I have given the 2-day MATLAB course in spring and fall for the past ten years, but this year it was given a third time as a command performance for the Laboratory of Neuropsychology at NIMH. The current version, MATLAB 5, is a major expansion of the language, and is taxing the 2-day format. For the first time this year, the course will be expanded to 3 days, and the content will be expanded to include graphics and user interfaces. This will require "revising an extensive set of class notes. - Signal processing, biochemical kinetics, DNA microarray analysis, Mathematical software.